1. Field of the Invention
An aspect of this disclosure relates to a function generator circuit.
2. Description of the Related Art
FIG. 1 is a circuit diagram of a temperature-compensated crystal oscillator (TCXO) 50 including a temperature compensating circuit 20 that functions as a function generator circuit. The temperature compensating circuit 20 outputs a control voltage Vc for an oscillating circuit 30 that causes an AT-cut quartz crystal 35 to oscillate. The TCXO 50 is implemented as an integrated circuit (IC). An oscillation frequency f of the quartz crystal 35 has a temperature characteristic represented by a cubic curve as illustrated in FIG. 2. When f0 indicates a natural resonance frequency at the temperature at an inflection point of the cubic curve, the vertical axis in FIG. 2 indicates a frequency error (f/f0) in the natural resonance frequency f0 caused by a temperature change. The temperature characteristic of the oscillation frequency f of the quartz crystal 35 is represented by a cubic function of formula (1) below.f=a(T−T0)3+b(T−T0)+c  (1)
In formula (1), “T” indicates a (ambient) temperature, “T0” indicates a temperature (central reference temperature or inflection point temperature) at the inflection point of the cubic curve, “a” indicates a coefficient for the third-order (cubic) term, “b” indicates a slope coefficient of the temperature characteristic, and “c” indicates an offset coefficient of the oscillation frequency f.
To prevent or reduce variations in the oscillation frequency f due to temperature changes, the oscillating circuit 30 includes variable-capacitance elements 31 and 32 for adjusting the oscillation frequency f. The control voltage Vc that varies depending on the ambient temperature T is applied to the variable-capacitance elements 31 and 32. The temperature compensating circuit 20 generates the control voltage Vc based on the ambient temperature T and applies the generated control voltage Vc to the variable-capacitance elements 31 and 32 to offset the temperature characteristic of the oscillation frequency f of the quartz crystal 35 and thereby compensate for the variation in the oscillation frequency f of the quartz crystal 35 caused by a temperature change.
The control voltage Vc is obtained by adding voltages generated by a third-order component generating circuit 6, a first-order component generating circuit 5, and a zeroth-order component generating circuit 4 and is approximated by a cubic function represented by formula (2) below.Vc=α(T−T0)3+β(T−T0)+γ  (2)
In formula (2), α indicates a coefficient of the third-order term, β indicates a coefficient of the first-order term, and γ indicates a coefficient of the zeroth-order term. Defining a cubic function using T0 as in formula (2) makes it possible to omit the second-order term and thereby makes it possible to reduce the size of the temperature compensating circuit 20. The variations in the oscillation frequency f of the quartz crystal 35 due to temperature changes can be compensated for by adjusting α, β, γ, and T0 in formula (2).
A T0 adjusting circuit 3 adjusts T0. The T0 adjusting circuit 3 adjusts T0 in formula (2) to match a temperature at the inflection point that is determined by the temperature characteristic of the quartz crystal 35.
Technologies related to function generator circuits are disclosed, for example, in Japanese Patent No. 4070139, Japanese Laid-Open Patent Publication No. 2007-325033, and Japanese Laid-Open Patent Publication No. 08-116214.
Here, as illustrated in FIGS. 3 (a) and (b), even if the inflection point temperature T0 is adjusted by the T0 adjusting circuit 3, the temperature at the inflection point of the control voltage Vc actually generated by a function generator circuit may be shifted from T0 to T0′ due to manufacturing variations of the function generator circuit. As illustrated in FIG. 3 (c), such a shift of T0 due to manufacturing variations results in a second-order component in the oscillation frequency f that has been corrected by the control voltage Vc.